a) Determine the zeros of the following systems and indicate whether the system is min, max or mic=xed phase.

1) $H_1(z)$ = 6 + $Z^{-1}$ + $6Z^{-2}$

2) $H_2(z)$ = 1 - $Z^{-1}$ - $6Z^{-2}$

b) Define group delay and phase delay.

c) Compare FIR and IIR filters.

d) What is frequency warping in bilinear transformation.

a) Compute DFT of sequence x(n) = {2,1,2,1,1,2,1,2} using DIT-FFT algorithm.

a) A low pass filter is to be designed with following desired frequency response.

Hd($e^{jw}$) = $E^{-j2w}$

= 0

Determine the filter coefficients $h_d(n)$ if the window function is defined as w(n) = 1

= 0

Also determine the frequency response H($e^{jw}$) of the designed filter.

a) The transfer function for discrete time system is given as

H(z) = $\frac{1+ 1/2 Z^{-1}}{1-3/4Z^{-1} + 1/8Z^{-2}}$

i) Draw Direct form I and form II realization

ii) Draw cascaded and parallel form realization

b) Explain subband coding of speech signal as a application of multirate signal processing.

a) Develop composite radix DITFFT flow graph for N= 6= 2x3.

b) Design a digital Butterworth filter that satisfies following constraints using bilinear transformation method. Assume Ts = 1s.

0.9 < |H($e^{jw}$)| <1

|H($e^{jw}$)| < 0.2

a) Show the mapping from S plane to Z plane using impluse invariant mehod. Explain its limitations. Using this method determine H(z) if

H(s) = $\frac{10}{(s+5)(s+2)}$ if Ts = 0.2s.

b) If x(n) = {1,2,3} and h(n) = {1,0}

1) Find linear convolution using circular convolution

2) Find circular convolution using DFT - IDFT.

a) Musical Sound Processing

b) Dual tone multi frequency signal detection

c) Subband Coding of speech signals